The animating figure behind the Great Synthesis (which fused Darwin's biology and Mendel's laws), Sir Ronald Aylmer Fisher was a polymath. Cambridge trained as a mathematician, he fell in with the "wrong crowd" - geneticists. He took up genetics, and in the process wound-up revolutionizing evolutionary theory - by co-inventing a branch of biology known as Population Genetics.
In 1901 - after the rediscovery of Mendel's laws, Darwin's theory was refuted (or at least displaced temporarily). Mendelians contended that the "new genetic laws" explained the fossil record, speciation and the spectrum of genetic diversity found in nature - better than Darwin's theory did. Less than two decades later (1918), population genetics drove a spike into the Mendelian coffin. Fisher's hypothesis predicts that Mendel's laws of inheritance produce small and gradual genetic shifts in a population over a short period of time (and such shifts sum up into speciation events over a long period of time). These Darwinian outcomes resulting from Mendel's laws collided with the mutationists' prediction (or more accurately their retrodiction) that new species arise - rapidly, all-of-a-sudden and randomly. Population genetics, almost single-handedly, blew apart the anti-Darwinian, saltationist lock on biology.
With the exception of Darwin's Origin of Species - Fisher's 1918 paper, The Correlation Between Relatives on the Supposition of Mendelian Inheritance, is, perhaps, the most consequential writing in the history of evolutionary biology. In it, he unpacked evolution as "a shift of an allele frequency in a population over a period of time". 
Regarding evolution, Fisher had another world-shaking idea - which was not fully appreciated until the late 1980s. Sexual selection (SS), though embraced by both Darwinians and Mendelians, neither faction took it seriously as a prominent evolutionary driver. Fisher was the second scientist (after Darwin) to grasp the salience of SS. He was the first to predict that the mate preferences of one sex for traits displayed by the opposite sex were under "genic control". Due to the explosion in the knowledge of genetics within the last two decades, there is a body of evidence emerging that SS - in some species - is the dominant driver of evolution.
Before the publication of the Origin, Darwin noticed that evolution was problematic with natural selection (NS) as its near-exclusive driver. In the Origin, he briefly touched on aspects of SS. One of his articulated reasons behind writing the Descent of Man was to correct what he saw was a fatal deficiency in the theory. 
Without SS as part of evolutionary theory, what exists in nature is under-explained by it. Genetic diversity cannot be accounted for by NS alone. Darwin declared outright that the "bright plumage of male birds", birdsong, massive antler racks on deer and elk, "odoriferous glands" in male insects, many other "male ornaments", and the sizes, colors and structural differences between males and females could not have arisen solely by NS. 
(NS cannot explain the appearance and preservation of "male ornaments" in nature - because they do not convey obvious survival advantages on male's carrying them, but SS does explain them - because they do convey reproductive advantages on males.)
" the advantages which favoured males derive from conquering other males in battle or courtship, and thus leaving a numerous progeny, are in the long run greater than those derived from rather more perfect adaptation to their conditions of life." -- Darwin
Fisher took Darwin - relatively at face value, cobbling together a model of SS derived from passages in the Descent. Under Fisher's model, not only males but females selecting for these traits and their offspring are conferred reproductive advantages. (According to more recent SS models, Fisher may have "jumped the gun" regarding the latter two predictions. He overgeneralized from sparse - if any - data.)
Fisher named his model of SS "runaway". Both the "exaggerated traits" shown by males and the preferences for the traits among females are reinforced through a positive feedback mechanism. Over time however, the intensity of female preferences for male traits (and the magnitude of these traits expressed by males) are checked by counter-selection pressures. Fisher maintained that these pressures nearly counter-balance the survival disadvantages conveyed on males carrying these traits.
From The Genetical Theory of Natural Selection (1930):
In 1929, the process of genetic drift was identified by Sewall Wright. To refresh -
Fisher had an almost inexplicable animus towards drift. He out-shouted and brow-beat any prominent biologist who dared look favourably on it as an important clue to explain or "contribute significantly to evolution". Reading between the lines of Fisher's papers and gauging his personality, now I think I understand why: Fisher did not want any sort of non-regularity to play much of a role in evolution. He liked the clean and relatively precise, non-random drivers of NS and SS. To Fisher, NS was part calculating machine and part pruning shears, subtracting and cutting the unruly branches of variation down to a formalized, Platonic beauty - where homozygous genotypes dominate large populations. Fisher was, above all else, a mathematician. However, the failure to look at evidence as evidence is the fatal flaw for any scientist. When Darwin realized that his theory crashed without SS as a consequential evo-driver, he took great pains to revise it, further delaying the publication of the Origin.
Insofar as the relative abundance of variation in nature is concerned, let's seek to reconcile Fisher's variation-pruning selection with that of Kimura's variation-generating randomness - by appealing to different levels of explanation. Examine these polar-opposite, theoretical extremes: (1) under Fisher's "mass selection" model, NS non-randomly slices variation down to a twig - under which organisms in large populations, carry only one optimal "wild-type"  allele per locus and (2) under Kimura's micro randomness model, neutral mutations generate immense variation and "some if not most of the changes in the genetic material are caused by genetic drift.". One might be tempted to say that "pruning" selection on the macroscopic (the population or even the organism) level is compatible - somehow - with "generative" randomness on the molecular level - because the two theories refer to distinct levels of reality. However, Fisher's model does not appear to picture what exists in nature, and if the "neutral model of evolution" (with drift as its super-dominant driver) were true, then similarly, would nature really look as it does? 
In conclusion, Fisher was both a genius and an ideologue. He brought Darwin back from the dead with population genetics, but he exerted an imperious control over other scientists - whom he thought his inferiors. Perhaps, this character flaw delayed the recognition of drift in evolution for 40 years. Fisher, also, visibly campaigned for forced sterilization laws. These laws targeted those he felt "genetically unfit". Those - who by carrying a "genetic load" - were destructive to the process of civilization itself. According to Fisher - however, the "genetic load" he carried around was - of course - benign.
(1) For decades - when it was un-popular, Ernst Mayr derisively labeled population geneticists "glorified bean counters", "bean baggers", etc. In horror, Mayr recoiled at the notion that evolution be described as "a shift of an allele frequency in a population over a period of time". To Mayr, this descriptor turned evolution precisely on its head. For him, evolution had to do with the sum-total of variation and diversity observed in nature, triggered by the generation-by-generation genetic changes experienced by individual organisms. To Mayr, a shift of an allele frequency in a population is the consequence of evolution.
"For Darwin and most evolutionists since 1859 the individual organism was the principal object of selection. The individual is the entity which survives or not, which reproduces or not, and which reproduces successfully or not." -- Mayr
(2) In "The Variation of Animals and Plants Under Domestication" (1868), Darwin (in addition to NS) tapped "pangenesis" as a short-term driver of evolution. According to his theory, beneficial characteristics acquired during the life of an organism could be passed onto offspring. Particles called "gemmules" shed by body cells became localized in the reproductive organs; Thus, evolution could be pushed over the course of a few generations.
"Darwin presented an incredibly detailed and clear description of sexual selection in The Descent of Man. Even though Darwin's account of sexual selection was by no means complete and he had a garbled understanding of inheritance, Darwin was correct about almost every topic related to sexual selection that he discussed. For instance, he laid out essentially the modern version of intrasexual selection, and he correctly realized that female choice was an important mechanism in sexual selection. He also recognized that sexual selection could sometimes act on both sexes or more strongly on females than on males, and he demonstrated a good intuitive understanding of the effects of the operational sex ratio and mating systems on the intensity of sexual selection." -- Adam G. Jones and Nicholas L. Ratterman 2009
(4) An allele which occurs naturally in wild populations at a relatively high frequency. This phrase is taken to represent how such an allele normally operates in individuals within natural (non-theoretical) populations.
(5) Non-Darwinian evolution: Most evolutionary change may be due to neutral mutations and genetic drift (1969), Jack Lester King and Thomas H. Jukes